Find the color at a particular surface point on a mesh
Particle System


You can generate cubes or other as particles.
Convert them in the modifier panel.
Join them into Single Mesh
Vertex [Remove Doubles] may produce large surfaces if desired




Above image. Plane with UV Map Bounds.  Particle System Grid Resolution 50.  Adjust to Needs.



Image above. Particle System Texture affects density. Blender Internal Render.



Image Above. Converted Particles with [Convert] in Edit Mode.



Image Above. Vertex Remove Doubles with a Tolerance. Only the top surface had Remove Doubles. The original cubes had spaces for sake of explanation



Above image.  Sphere shape which is a high density Cube to Sphere Transform.  UV Mapped while in Cube appearance.  Thus 6 repeating UV faces even though the repetition is difficult to see.